What is the name of your state (only U.S. law)?
The only way that would happen would be if he remarried his ex and became the legal father via stepparent adoption, or if Mom terminates her own rights allowing your son to adopt as a single parent.
I doubt she'd be on board for that so that leaves option 1. He should not do this - at all. Ever. Even if. And if Mom comes back and says that's the only way he can see the child, that's a huge red flag with "I only want your money because if this was about what's best for my son I'd be fine with you having a play-date with him from time to time to continue the relationship and no adoption would be necessary" written on it.